I can't speak for customer service because I have not reached out or used that service with Zip Recruiter but here is my general experience thus far.
Submit an application, and go on with your life, forgetting you even applied, because no employer will even reply. - That is the catchphrase I would float to the company in a marketing meeting. Because that's the reality of Zip Recruiter.
Imagine a convenient service where you can go to view jobs of pretty much any industry, Read job descriptions, apply and have one place to manage your applications. Like, say, LinkedIn, but specific to just jobs and not networking. It sounds great and even has a cool name. Even the word 'Recruiter' is in the name, so it's pretty clear what they are doing. Unless you imagine they're only hiring for sewing jobs on a specific portion of clothing fasteners, but I digress. This model isn't exactly new. Indeed was around, there was Monster for the longest time. Sadly, the idea seems to be a pipe dream. I mean that like, somebody is hitting the pipe over there at Zip Recruiter.
I can probably go look at the data and tell you exactly how many jobs I applied for over time, but my overall experience is that it doesn't matter because if I get any contact beyond "We are so grateful to have received your application/interest in this job" Then I can't remember any. No rejections, no interviews, no idea what happened to my submission. As far as I can tell, either a bunch of people have my resume and personal information, or Zip Recruiter has a ton of documents with my personal information in a database somewhere.
I wish it felt more alive than it does, but it seems this, and every other service like it, except LinkedIn where at least I get rejection notices, are just trying to get you to fill out applications. They never produce any kind of result within any kind of time frame that allows you to feel like it is doing anything valid for your job search.
I sincerely wish this were not the case, because I do like the feature of getting job notifications in my email. It's like hope on a schedule, but it has become just as spammy as the guy with the extra diamonds he can't sell.